A Mathematician Wears a Bracelet

For my birthday this year, my son fashioned me a bracelet out of a pipe cleaner and some glittery green beads. There was just one problem, though:

He didn’t account for his dad’s big hands.

Lucky for me, I’m a mathematician, and I know the Isoperimetric Theorem.

The Isoperimetric Theorem: Among all closed curves with a given perimeter, the one with the biggest area is the circle.

If the bracelet had been elastic, like made from a rubber band, I could have just pulled to lengthen it at gotten it around my wrist. But the pipe cleaner didn’t have any give that way – its length was fixed. It was flexible, though, so I was free to reshape the bracelet into whatever form would let my hand pass through. I could have made it into a square…

…or a star…

…or a circle…

…or something else. However, the Isoperimetric Theorem told me that the circle would give the largest area to push a hand through. In fact, the square only had 78.5% of the circle’s area, and the star, with only 53.6% of the circle’s area, would be a particularly unwise choice.

Unfortunately, just making a bracelet circular is not enough. Even though the bracelet was optimized for area efficiency, my hand was not.